What's the most damage you can deal? This was the question we asked ourselves, and this article describes the outcome of our mad science.
We put 2^2059 copies of Doubling Season into play (that's a lot).
...and then we tap Serra's Sanctum
for
66,185,228,434,044,942,951,864,067,458,396,061,614,989,522,267,577,311,297,802,947,435,570,493,724,401,440,549,267,868,490,798,926,773,634,494,383,968,047,143,923,956,857,140,205,406,402,740,536,087,446,083,831,052,036,848,232,439,995,904,404,992,798,007,514,718,326,043,410,570,379,830,870,463,780,085,260,619,444,417,205,199,197,123,751,210,704,970,352,727,833,755,425,876,102,776,028,267,313,405,809,429,548,880,554,782,040,765,277,562,828,362,884,238,325,465,448,520,348,307,574,943,345,990,309,941,642,666,926,723,379,729,598,185,834,735,054,732,500,415,409,883,868,361,423,159,913,770,812,218,772,711,901,772,249,553,153,402,287,759,789,517,121,744,336,755,350,465,901,655,205,184,917,370,974,202,405,586,941,211,065,395,540,765,567,663,193,297,173,367,254,230,313,612,244,182,941,999,500,402,388,195,450,053,080,385,548
mana.
And then we use
Djinn Illuminatus
to replicate
Burst of Energy,
untapping Kiki-Jiki
66,185,228,434,044,942,951,864,067,458,396,061,614,989,522,267,577,311,297,802,947,435,570,493,724,401,440,549,267,868,490,798,926,773,634,494,383,968,047,143,923,956,857,140,205,406,402,740,536,087,446,083,831,052,036,848,232,439,995,904,404,992,798,007,514,718,326,043,410,570,379,830,870,463,780,085,260,619,444,417,205,199,197,123,751,210,704,970,352,727,833,755,425,876,102,776,028,267,313,405,809,429,548,880,554,782,040,765,277,562,828,362,884,238,325,465,448,520,348,307,574,943,345,990,309,941,642,666,926,723,379,729,598,185,834,735,054,732,500,415,409,883,868,361,423,159,913,770,812,218,772,711,901,772,249,553,153,402,287,759,789,517,121,744,336,755,350,465,901,655,205,184,917,370,974,202,405,586,941,211,065,395,540,765,567,663,193,297,173,367,254,230,313,612,244,182,941,999,500,402,388,195,450,053,080,385,548
times
(and every time Kiki-Jiki untaps, we're going to tap him again to copy more
Doubling Seasons!)
Time-out for a moment, audience check: if you're grinning with glee right now, this article is probably for you, stick around and grab some popcorn. On the other hand if you're hissing, holding up garlic to the screen, and yelling 'the math, it burns!' trust me: it's only going to get worse. Get out now while you still can!
'repeat this action until you run out of [resource]'.
In the case above, the first layer was the copies of Burst of Energy on the stack:
'Untap Kiki-Jiki and copy a Doubling season for each Burst of Energy on the stack'
The second layer was the number of Fossil Finds on the stack:
'Tap Serra's Sanctum and replicate Burst of Energy a LOT of times for each Fossil Find on the stack'
Now, note that some of our earlier builds were running cards like Mycosynth Lattice--this meant that instead of having six different kinds of mana (all five colours and colourless) we had a single kind of mana, and therefore fewer total resource pools. And with fewer resource pools we got fewer layers of recursion (i.e. we couldn't say 'do [task] until you run out of green mana').
5+5 = 5 + 1 + 1 + 1 + 1 + 1.
5*5 = 5 + 5 + 5 + 5 + 5.
5^5 = 5 * 5 * 5 * 5 * 5.
The philosophy behind Knuth's up arrow notation is 'why stop at three functions?'
5^^5 = 5^(5^(5^(5^5))).
5^^^5 = 5^^(5^^(5^^(5^^5))).
5^^^^5 = 5^^^(5^^^(5^^^(5^^^5))).
And so on. So, okay, let's remember our Doubling Season example above. Each time Kiki-Jiki copied Doubling Season, it counted X the previous number of Doubling Seasons, and adds 2^X more. Ignoring the adding part (which becomes insignificant pretty fast) it just does a 2^X increase. So if we do a copy with each of the four Kiki-Jikis, we get roughly 2^(2^(2^(2^2)))) = 2^^5. When we replicated Burst of energy 2^2059 times, what we got was something more-like 2^^( 2^2059 ). And then if we added in the replicated Fossil Find layer above all that, that means we're doing the 2^^() effect from Burst of Energy over and over, i.e. 2^^(2^^(2^^(2^^(...)))). Though hey, that looks familiar--in fact it looks rather like 2^^^(X). And then if we had some way to repeatedly bring back Fossil Find, we could up the ante again by doing 2^^^(2^^^(2^^^(...))), or roughly 2^^^^X.
Don't spend too much time worrying about what these numbers actually look like.
Suffice it to say...
1. The numbers quickly get wayyyyyyy bigger than anything you could write in Scientific notation.
2. The only really important thing to watch is how many layers of recursion there are. Finding a way
to spend two mana instead of three on a spell you're replicating quickly becomes barely-noticeable when
the numbers are so large.
Finding a way to cast your best spell a zillion times, however, is always a big deal (especially
since you get a LOT more mana for the next replication after each casting).
Remember, all luck is with us, not just a stacked deck, so we win all our coinflips and draw 50 cards. No need to count cards anymore!
Eureka (14 life, WB left in pool)
At this point, use Eureka to put all our permanents from our deck into the battlefield (Minion Reflector, Opalescence, March of the Machines, Nature's Revolt, Doubling Season, Kiki-Jiki, Rings of Brighthearth, Mana Reflection, Copy Enchantment (copying Doubling Season), Hammerheim, Savannah, Steward of Valeron, Llanowar Dead, Apprentice Wizard, Ęther Spellbomb, Mirror Gallery, Vedalken Orrery, Djinn Illuminatus, Holistic Wisdom).
We now have multiple Minion Reflector triggers, with Channel being the only way to pay for them. These are the ones to pay for:
Hammerheim (12 life) (not an option--need red sources since only our red spells can get us more red mana. Remember, the original
Hammerheim will have summoning sickness, so if we don't copy it we can't produce red mana at all. However, copies of Hammerheim
made with Minion Reflector will have haste).
Lucrezia (10 life) (Kiki-Jiki can't copy her, and we're out of blue mana)
Kiki-Jiki (8 life) (not strictly needed because he has haste, but he's awesome).
Kiki-Jiki should tap to copy Doubling Season (we already have two, so we get 2^2 = 4 copies). Or, actually we may as well pay 2 more life (6 life) to use Rings of Brighthearth to copy Kiki-Jiki's ability, getting us a total of 2 + 4 + 2^6 = 70 Doubling Seasons. Now resolve Kiki-Jiki's Minion Reflector trigger, putting 2^70 = 1,180,591,620,717,411,303,424 Kiki-Jikis into play. From here, we can use five Kiki-Jiki taps to get hasty versions of all of our mana producers and also Ęther Spellbomb (we can't bounce and replay Ęther Spellbomb itself if we don't have extra copies of Ęther Spellbomb). From here all the combo pieces are online, so follow the steps below.
* Channel: we have no source of life gain right now
* Eureka: With the number of permanents this deck has, it's a spell that adds maybe 100 mana. Once we
get going we'll have spells that add much, much more mana than that.
* Channel the Suns: once again, we will have spells that add effectively much more mana (thanks to Mana Reflection)
* Black Lotus: It's a spell that adds 3 mana. As an artifact, it's a permanent that can't be copied. If March of the Machines
is in play, it becomes an Artifact Creature, but does not trigger Minion Reflector because it dies
as a state-based effect from being 0/0 before triggered abilities can go on the stack.
* Squee's Revenge: only 53 cards to draw in the deck (and it can only draw 52!)
Tap one of your many Apprentice Wizard for 2^(2^(X))*3 (UUU used). Bounce (UUUU used) and replay Minion Reflector, paying the 2 to get a token (so that we get 2^X Minion Reflectors).
Bounce and replay Copy Enchantment, this time copying Doubling Season (UUUUUU), and pay 2 for EVERY Minion reflector you control costing us (2^X)*2 colourless mana (though remember we've got 2^(2^(X))*3 in our mana pool--we can afford it). Now we have 2^X Doubling Seasons tokens entering the battlefield one at a time. Each one will 2^X the number of Doubling Seasons, meaning the next token to enter the battlefield makes even more tokens, so we get... 2^(2^(2^(2^(...^(2^X)...)))), or roughly 2^^X.
One last trick, not strictly necessary, but you can pay all 2^^(2^X) Minion Reflector triggers on Mana Reflection, and then let them resolve one at a time, using Vedalken Orrery to do steps 1 and 2 at instant speed in between each Minion Reflection token coming into the battlefield. Just reduces the cost of each Doubling Season bounce cycle to UUUU instead of UUUUUU.
...Anyway, we're tapping Lucrezia for 2^(2^X) blue mana, and for every four blue mana we 2^^X the number of doubling seasons, so overall we're looking at 2^^(2^^(2^^(2^^...(2^^X)...))) which gives us 2^^^X.
Anyway when we're almost out of blue mana, we can spend ONE black mana to get a LOT of blue. Here's how: bounce Lucrezia, and replay her, paying for every single Minion Reflector trigger so that there are X triggers on the stack. Let one trigger resolve, putting X hasty copies of Lucrezia into the battlefield. Each time we tap a Lucrezia for blue mana, we make the Doubling Season and Mana Reflection count go from X to 2^^^X. So going through all the Lucrezias that just entered the battlefield will give us 2^^^(2^^^(2^^^(...^^^X...))) = 2^^^^X.
However, THAT was just a single Minion Reflector trigger. Now let a second trigger resolve, and we put 2^^^^X copies of Lucrezia into play. Repeat the above, then let another trigger resolve, and we put 2^^^^(2^^^^X) copies of Lucrezia into play. In total over all X triggers we effectively do 2^^^^^X.
To note here--all higher levels of recursion will be spells, and not permanents that could be targetted with Heat Shimmer. This prevents going infinite using any of the combo pieces in-play.
Note that replicate has largely removed any use for Storm in this deck. They both trigger off of casting a spell, and trigger at the same time. And for the curious--no multiple instances of replicate don't stack--replicate triggers off of paying additional costs at the time of casting.
Now, due to the way the stack works, the replicate copies resolve first, and then the Fossil Find finally resolves, putting it in the graveyard. None of the copies nor the original spell can return the actual Fossil Find card, so we don't go infinite.
Everytime we replicate Fossil Find, we get X castings of Radiate. This puts us at about 2^^^^^^^^^^^^^^^^^^^^^X.
* copy of Holistic Wisdom's activated ability
* Rings of Brighthearth triggered ability
* Rings of Brighthearth triggered ability
* Rings of Brighthearth triggered ability
...
* Rings of Brighthearth triggered ability
* Rings of Brighthearth triggered ability
* Rings of Brighthearth triggered ability
* Holistic Wisdom's activated ability
So we can resolve one trigger each time Fossil Find hits the graveyard, and at the time we resolve the trigger we get to choose new targets for the copy. Hence the only copy that will fizzle to to a missing target is the original Holistic Wisdom activation.
Of course, being able to get X castings of Fossil Find means we get 2^^^^^^^^^^^^^^^^^^^^^^X.
Okay, so this is the final layer, we can afford to be a bit more precise. We have 33 cards left in the deck. We have 4 additional sorceries that we opened with but no longer need. We're also not starting from 0 before the first card is removed to Holistic Wisdom. In particular, one replication of Fossil Find gets us about 2^^...(21 arrows)...^^( kinda large number ). This is larger than 2^^...(22)...^^( 2 ) = 4, and larger than 2^^...(22)...^^( 3 ) = 2^^...(21)...^^( 4 ). However, it's probably smaller than or close to 2^^...(22)...^^( 4 ) = 2^^...(21)...^^( 2^^...(21)...^^( 4 ) ). However, that number is exactly equal to 2^^...(23)...^^( 3 ), so it seems like that's our starting point before we remove a single card with Holistic Wisdom; hence we'll add 3 to our 37 sorceries we're removing.
Final result: about 2^^^^^^^^^^^^^^^^^^^^^^^40.